Issue |
A&A
Volume 690, October 2024
|
|
---|---|---|
Article Number | A186 | |
Number of page(s) | 13 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/202450409 | |
Published online | 07 October 2024 |
Gravitational collapse at low to moderate Mach numbers: The relationship between star formation efficiency and the fraction of mass in the massive object
1
Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción,
Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C,
Concepción,
Chile
2
Universität Heidelberg, Zentrum für Astronomie, Institut für theoretische Astrophysik,
Albert-Ueberle Str. 2,
69120
Heidelberg,
Germany
3
Universität Heidelberg, Interdisziplinäres Zentrum für wissenschaftliches Rechnen,
Im Neuenheimer Feld 205,
69120
Heidelberg,
Germany
4
Max-Planck-Institut für Astrophysik,
Karl-Schwarzschild-Str. 1,
85748
Garching,
Germany
5
Astronomical Institute, Graduate School of Science, Tohoku University,
Aoba, Sendai
980-8578,
Japan
6
Centre for Astrophysics and Space Sciences Maynooth, Department of Theoretical Physics, Maynooth University,
Maynooth,
Ireland
7
Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik,
Albert-Ueberle-Str. 2,
69120
Heidelberg,
Germany
8
Department of Physics, University of Helsinki,
Gustaf Hällströmin katu 2, University of Helsinki,
00014
Finland
9
Centro de investigación en Astronomía, Facultad de Ingeniería, Ciencia y Tecnología, Universidad Bernardo O’Higgins,
Av. Viel 1497,
Santiago,
Chile
10
Hamburger Sternwarte, Universität Hamburg,
Gojenbergsweg 112,
21029
Hamburg,
Germany
★ Corresponding author; dschleicher@astro-udec.cl
Received:
16
April
2024
Accepted:
16
August
2024
The formation of massive objects via gravitational collapse is relevant both for explaining the origin of the first supermassive black holes and in the context of massive star formation. Here, we analyze simulations of the formation of massive objects pursued by different groups and in various environments, concerning the formation of supermassive black holes, primordial stars, as well as present-day massive stars. We focus here particularly on the regime of small virial parameters, that is, low ratios of the initial kinetic to gravitational energy, low to moderate Mach numbers, and the phase before feedback is very efficient. We compare the outcomes of collapse under different conditions using dimensionless parameters, particularly the star formation efficiency є*, the fraction ƒ* of mass in the most massive object relative to the total stellar mass, and the fraction ƒtot of mass of the most massive object as a function of the total mass. We find that in all simulations analyzed here, ƒtot increases as a function of є*, although the steepness of the increase depends on the environment. The relation between ƒ* and є* is found to be more complex and also strongly depends on the number of protostars present at the beginning of the simulations. We show that a collision parameter, estimated as the ratio of the system size divided by the typical collision length, allows us to approximately characterize whether collisions are important. A high collision parameter implies a steeper increase in the relation between ƒtot and є*. We analyze the statistical correlation between the dimensionless quantities using the Spearman coefficient and further confirm via a machine learning analysis that good predictions of ƒ* can be obtained from є* together with a rough estimate of the collision parameter. This suggests that a good estimate of the mass of the most massive object can be obtained once the maximum efficiency for a given environment is known and an estimate for the collision parameter has been determined.
Key words: methods: numerical / methods: statistical / quasars: supermassive black holes
© The Authors 2024
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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